Least Common Multiple (LCM) of 39 and 55
The least common multiple (LCM) of 39 and 55 is 2145.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 39 and 55?
First, calculate the GCD of 39 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 55 = 0 remainder 39 |
| 2 | 55 ÷ 39 = 1 remainder 16 |
| 3 | 39 ÷ 16 = 2 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 82 | 14022 |
| 34 and 199 | 6766 |
| 69 and 142 | 9798 |
| 86 and 74 | 3182 |
| 200 and 13 | 2600 |